You are forgetting that it later became the Holy Roman Empire and embraced/preserved Christianity.
I believe that can be debated. No, I’m not prepared to do so right now but clearly ‘Holy’ can be applied as well as ‘Christianity’ to most anything or anyone but that does not make it so. The Roman Empire (imo) falls into that category.
The Holy Roman Empire was a medieval German creation, founded long after the Western Empire fell. The old saying was that it was neither holy, nor Roman, nor an empire.